Ill-posed problems in probability and stability of random sums

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書誌事項

Ill-posed problems in probability and stability of random sums

Lev Klebanov, Tomasz J. Kozubowski, Svetlozar T. Rachev

Nova Science Publishers, c2006

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注記

Includes bibliographical references and indexes

内容説明・目次

内容説明

This volume is concerned with the problems in probability and statistics. Ill-posed problems are usually understood as those results where small changes in the assumptions lead to arbitrarily large changes in the conclusions. Such results are not very useful for practical applications where the presumptions usually hold only approximately (because even a slightest departure from the assumed model may produce an uncontrollable shift in the outcome). Often, the ill-posedness of certain practical problems is due to the lack of their precise mathematical formulation. Consequently, one can deal with such problems by replacing a given ill-posed problem with another, well-posed problem, which in some sense is 'close' to the original one. The goal in this book is to show that ill-posed problems are not just a mere curiosity in the contemporary theory of mathematical statistics and probability. On the contrary, such problems are quite common, and majority of classical results fall into this class. The objective of this book is to identify problems of this type, and re-formulate them more correctly. Thus, alternative (more precise in the above sense) versions are proposed of numerous classical theorems in the theory of probability and mathematical statistics. In addition, some non-standard problems are considered from this point of view.

目次

  • The General Form of Quantitative Convergence Criteria
  • Some Important New Classes of Probability Metrics
  • Convergence in Weak and Strong Metrics
  • Convergence to Prescribed Distributions
  • Ill-Posed Problems in Computer Tomography
  • Stable Probabilistic Schemes
  • Central Pre-Limit Theorems
  • Infinitely Divisible and Stable Distributions
  • Geometric Stable Distributions on the Real Line
  • Multivariate Geometric Stable Distributions
  • Geometric Stable Laws on Banach Space
  • Estimation and Empirical Issues for GS Distributions
  • A Generalisation of Stable Laws
  • Characterisations of Distributions in Reliability
  • Index.

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